surveillance: Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic Phenomena

Description Usage Arguments Details Value Author(s) See Also Examples

This function helps to construct a formula object that can be used in a call to hhh4 to model seasonal variation via a sum of sine and cosine terms.

1	addSeason2formula(f = ~1, S = 1, period = 52, timevar = "t")

`f`	formula that the seasonal terms should be added to, defaults to an intercept `~1`.
`S`	number of sine and cosine terms. If `S` is a vector, unit-specific seasonal terms are created.
`period`	period of the season, defaults to 52 for weekly data.
`timevar`	the time variable in the model. Defaults to `"t"`.

The function adds the seasonal terms

sum_s gamma_s * sin(2*pi*s/period * t) + delta_s * cos(2*pi*s/period * t),

where gamma_s and delta_s are the unknown parameters and t, t = 1, 2, … denotes the time variable timevar, to an existing formula f.

Note that the seasonal terms can also be expressed as

γ_s sin(2*pi*s/period * t) + δ_s cos2*pi*s/period * t) = A_s sin(2*pi*s/period * t + ε_s)

with amplitude A_s=sqrt{γ_s^2 +δ_s^2} and phase difference \tan(ε_s) = δ_s / γ_s.

Returns a formula with the seasonal terms added and its environment set to .GlobalEnv. Note that to use the resulting formula in hhh4, a time variable named as specified by the argument timevar must be available.

M. Paul, with contributions by S. Meyer

hhh4, fe, ri

# add 2 sine/cosine terms to a model with intercept and linear trend
addSeason2formula(f = ~ 1 + t, S = 2)

# the same for monthly data
addSeason2formula(f = ~ 1 + t, S = 2, period = 12)

# different number of seasons for a bivariate time series
addSeason2formula(f = ~ 1, S = c(3, 1), period = 52)